Many of the examples mentioned in the preceding section satisfy various closely-related finite type conditions [1]}, [2]}, [3]}, [4]}.
Heuristically, these finite type conditions require that there are only “finitely many overlaps”
These separation conditions are all special cases of the weak separation condition of Lau and Ngai [5]}, which states that there is a uniform bound on the number of simultaneous “distinct overlaps” (see e:wsc for a precise statement).
Note that the weak separation condition is strictly weaker than the open set condition.
When the invariant set \(\mu \)  is a closed interval, the generalized finite type condition coincides with the weak separation condition [6]}, [2]}.
It is an open question to determine, outside certain degenerate situations, if these two separation conditions are equivalent in general.
